It might have been a retro fit, where the previous owner removed the T8 sockets and replaced them with T5's because the housing definitely looks like a T8
IMO. Is it a 1 or 2 bulb fixture? And I think the length is like 32" bulb for a 36" T5 fixture but don't quote me on that as I have only ever had a 24" T5 and I replaced it just a few months after I got it.